In Section , two potential improvements that could be made to the process of finding a rank-maximal stable matching in an instance of smi were highlighted. First was the adaptation of [1]}'s [1]} Max Flow algorithm to work in the vector-based setting. This adaptation would result in a time complexity of \(O(nm^2)\)  to find a rank-maximal stable matching, improving on the method outlined in this paper by a factor of \(\log n\) , however it is not clear that [1]}'s algorithm can be adapted to the vb-flow setting. Additionally, [4]} used an entirely different technique based on weighted sat for finding a rank-maximal stable matching in \(O(n^{0.5}m^{1.5})\)  time. It remains to be seen if this could be adapted to work in the vector-based setting.
